Topos à l'IHES

Europe/Paris
Salle de Conférences Marilyn et James Simons (Le Bois-Marie)

Salle de Conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette
Description

The concept of topos was introduced by A. Grothendieck during his Séminaire de Géométrie Algébrique du Bois-Marie, which took place at the IHES in the early sixties. The original motivation was that of defining a general notion of space on which one could define cohomological invariants in the algebro-geometric setting needed for proving the Weil's conjectures. In spite of this quite specific technical motivation, the notion of topos appeared at the very beginning as defining a new conception of space, capable of unifying the continuous and the discrete in an harmonious marriage: in the words of Grothendieck "Un lit si vaste en effet (telle une vaste et paisible rivière très profonde...), que “tous les chevaux du roi y pourraient boire ensemble...". "
 
In the following years, new perspectives on the notion on topos emerged. According to Lawvere and Tierney, a topos can be considered not only as a generalized space but as a mathematical universe within which one can carry out most familiar set-theoretic constructions, but which also, thanks to the inherent ‘flexibility' of the notion of topos, can be profitably exploited to construct 'new mathematical worlds' having particular properties. On the other hand, the theory of classifying toposes allows to regard a Grothendieck topos as a suitable kind of first-order theory modulo Morita-equivalence. Toposes have also been proved effective in studying dualities and establishing ‘bridges’ across different mathematical theories with a related semantic content.  
 
The conference aims to illustrate the fruitfulness and wide-ranging impact of the notion of topos, by featuring presentations on new theoretical advances in the subject (including the theory of higher toposes) as well as on applications of toposes in different fields such as number theory, algebraic geometry, logic, functional analysis, topology, mathematical physics and computer science. The conference is preceded by a two-day introductory mini-course for the benefit of students and mathematicians who are not already familiar with topos theory.

Scientific committee : O. CARAMELLO*, P. CARTIER, A. CONNES, S. DUGOWSON, A. KHELIF

23-24 November : Tutorials by: Olivia CARAMELLO and André JOYAL

25-27 November : Invited speakers :

Mathieu ANEL (University Paris-Diderot)
Luca BARBIERI-VIALE (Università degli Studi di Milano)
Jean BÉNABOU (University Paris 13)
Caterina CONSANI (Johns Hopkins University, Baltimore)
Thierry COQUAND (University of Göteborg)
Simon HENRY (Radboud University, Nijmegen)
André JOYAL (Université du Quebec, Montréal)
Mike PREST (University of Manchester)
Urs SCHREIBER (Eduard Čech Institute for Algebra, Geometry and Physics, Prague)
Carlos SIMPSON (University of Nice-Sophia-Antipolis) 
Michel VAQUIÉ (University Paul Sabatier, Toulouse)

25 & 27 November: Short Communications Speakers

Ingo BLECHSCHMIDT (University of Augsburg)
Matias DATA (Universidad de Buenos Aires)
Jonas FREY (Copenhagen University)
Camell KACHOUR
Guilherme Frederico LIMA de CARVALHO e SILVA (University of Cambridge)
Pietro POLESELLO (Universita di Padova)
David ROBERTS (University of Adelaide)
Anna Carla RUSSO (University of Salerno & Université Paris-Diderot)
Alex SIMPSON (University of Ljubljana)
Zoran  SKODA (University of Hradec Kralové)
Christopher TOWNSEND (Royal Bank of Canada)

* holder of a fellowship "L'Oréal-Unesco for Women in Science" which supports the conference
 


The non-official website of the conference  ­(maintained by S. Dugowson)
contains further materials provided by the speakers
­in connection with their talks and edited versions of the videos of the tutorials.


logos

Poster
Participants
  • Alain Connes
  • Alex Simpson
  • Alexander Gietelink Oldenziel
  • Ambroise Peugeot
  • Anatole Khelif
  • Andrea Gagna
  • Andrew Polonsky
  • André Joyal
  • Angel Israel Toledo
  • Anna Carla Russo
  • Anthony Bordg
  • Armajac Raventós i Pujol
  • Aurélien SAGNIER
  • Bruno Blind
  • Bruno Stonek
  • Bruno Vallette
  • Camell Kachour
  • Carlos Simpson
  • Carolina Rivera Arredondo
  • Caterina Consani
  • Charles ALUNNI
  • Christopher Townsend
  • CYRIL POREE
  • Cyrus Cohier-Chevaux
  • Céline Loozen
  • Daniel Luckhardt
  • Danko Ilik
  • David Gepner
  • David Rabouin
  • David Roberts
  • Diana Catalina Ossa Orozco
  • Dimitris Scarpalezos
  • Domenico Ruoppolo
  • elisabeth vaugelade
  • Fabio Pasquali
  • Fabrizio Anella
  • Federico Zalamea
  • Francesco Meazzini
  • Frank Taipe
  • Frédéric Crozatier
  • Gabriel Catren
  • Georg Lehner
  • Guilherme Frederico Lima de Carvalho e Silva
  • henri lombardi
  • himanee arjunwadkar
  • Hugh Steele
  • Ingo Blechschmidt
  • Isar Stubbe
  • Jacqueline Zizi
  • Jean Benabou
  • Jean Petitot
  • Jean-Jacques szczeciniarz
  • Jeffrey Egger
  • Jonas Frey
  • Joost van Dijk
  • Juan-Pablo Vigneaux
  • Julien Page
  • Jun Maillard
  • Kenji Maillard
  • Laurence Honnorat
  • Laurent Lafforgue
  • Laurent Tsang
  • Luca Barbieri-Viale
  • Lucile Regourd
  • Lucius Schoenbaum
  • Luigi Lunardon
  • Marco Robalo
  • Marie Bjerrum
  • Mathieu Anel
  • Matias Data
  • Mauro Mantegazza
  • Maxim Kontsevich
  • Mehdi Zaidi
  • Michael Heather
  • Michael Lambert
  • Michael Wright
  • Michel Hilsum
  • Michel Lapidus
  • Michel Vaquié
  • Mijail Guillemard
  • Mikaël Monchicourt
  • Mike Prest
  • Ngo Quoc Hoan
  • Nicolás Canevali
  • Nicolás Ramírez Díaz
  • Ofer Gabber
  • Olivia Caramello
  • Omar Mohsen
  • Pablo Sanchez Ocal
  • Paul LESCOT
  • Paula Verdugo
  • Pierre Cagne
  • Pierre Cartier
  • Pierre Schapira
  • Pietro Polesello
  • Pol van Hoften
  • Rafaël Bocquet
  • Rehan MALAK
  • Robert Olivares
  • Samir Bouslamti
  • Sandra Mantovani
  • Serge Bouc
  • Shai Haran
  • Simon Henry
  • Snorre Harald Christiansen
  • Stefan Neuwirth
  • Stefano Guerrini
  • Stéphane Bailly
  • Stéphane Dugowson
  • Thierry Coquand
  • Urs Schreiber
  • Vincent Picouet
  • Yuri Sulyma
  • Zoran Skoda
    • 08:30 17:00
      Lundi 23 novembre
      • 08:30
        Accueil des participants 30m
      • 09:00
        Ouverture de la conférence par Olivia CARAMELLO 5m
      • 09:05
        Pierre CARTIER 1h 10m
        Conférence inaugurale
        Abstract
      • 10:15
        André JOYAL 1h 15m
        A crash course in topos theory : the big picture (I)
        Programme
      • 11:30
        Pause-café 15m
      • 11:45
        André JOYAL 45m
        A crash course in topos theory : the big picture (II)
      • 12:30
        Lunch 1h 30m
      • 14:00
        Olivia CARAMELLO 1h 15m
        Introduction to categorical logic, classifying toposes and the « bridge » technique (I)
        Programme
      • 15:15
        Pause café 30m
      • 15:45
        Olivia CARAMELLO 1h 15m
        Introduction to categorical logic, classifying toposes and the « bridge » technique (II)
    • 09:00 17:00
      tuesday
      • 09:00
        Café d'accueil 30m
      • 09:30
        André JOYAL 1h 15m
        A crash course in topos theory : the big picture (III)
      • 10:45
        Pause café 30m
      • 11:15
        André JOYAL 1h 15m
        A crash course in topos theory : the big picture (IV)
      • 12:30
        Lunch 1h 30m
      • 14:00
        Olivia CARAMELLO 1h 15m
        Introduction to categorical logic, classifying toposes and the « bridge » technique (III)
      • 15:15
        Pause café 30m
      • 15:45
        Olivia CARAMELLO 1h 15m
        Introduction to categorical logic, classifying toposes and the « bridge » technique (IV)
    • 09:30 16:30
      wednesday
      • 09:30
        Welcome coffee 30m
      • 10:00
        Michel VAQUIÉ 1h
        Théorie spectrale en géométrie relative
        Résumé
      • 11:00
        Coffee break 15m
      • 11:15
        Caterina CONSANI 1h 15m
        On the geometry of the adele class space of Q
        Abstract
      • 12:30
        Lunch 1h 30m
      • 14:00
        Mathieu ANEL 1h 15m
        Toposes are commutative rings
        Abstract
      • 15:15
        Simon HENRY 1h
        Operator algebras from toposes
        Abstract
      • 16:15
        Pause café 15m
    • 16:30 18:00
      Courtes Communications - CCMJS: test subtitle

      Courtes communications (30') en 2 sessions parallèles: Centre de conférences Marilyn et James Simons

      • 16:30
        Guilherme-Frederico LIMA DE CARVALHO E SILVA 30m
        From Essential Inclusions to Local Geometric Morphisms
        Abstract
      • 17:00
        Anna Carla RUSSO 30m
        Morita-equivalences for MV-algebras
        Abstract
      • 17:30
        Christopher F. TOWNSEND 30m
        There are categories of ‘spaces' that are not categories of locales
        Abstract
    • 16:30 18:00
      Courtes Présentations - Amphi Motchane: test sub

      Courtes communications (30') en 2 sessions parallèles : Amphithéâtre Léon Motchane

      • 16:30
        Pietro POLESELLO 30m Amphithéâtre Léon Motchane

        Amphithéâtre Léon Motchane

        Le Bois-Marie

        35, route de Chartres 91440 Bures-sur-Yvette
        Proper stacks and costacks
        Abstract
      • 17:00
        Jonas FREY 30m Amphithéâtre Léon Motchane

        Amphithéâtre Léon Motchane

        Le Bois-Marie

        35, route de Chartres 91440 Bures-sur-Yvette
        Realizability toposes as homotopy categories
        Abstract
      • 17:30
        Zoran SKODA 30m Amphithéâtre Léon Motchane

        Amphithéâtre Léon Motchane

        Le Bois-Marie

        35, route de Chartres 91440 Bures-sur-Yvette
        Localizations and semiquantals
        Abstract
    • 09:30 16:15
      thursday
      • 09:30
        Welcome coffee 30m
      • 10:00
        Carlos SIMPSON 1h
        Pre-buildings as sheaves on the site of enclosures
        Abstract
      • 11:00
        Coffee break 15m
      • 11:15
        Mike PREST 1h 15m
        Model-theoretic imaginaries and localisation for additive categories
        Abstract
      • 12:30
        Lunch 1h 30m
      • 14:00
        André JOYAL 1h 15m
        New variations on the notion of topos
        Abstract
      • 15:15
        Luca BARBIERI-VIALE 1h
        T-Motives
        Abstract
    • 09:30 16:30
      friday
      • 09:30
        Welcome coffee 30m
      • 10:00
        Thierry COQUAND 1h
        Logic and topology
        Abstract
      • 11:00
        Coffee break 15m
      • 11:15
        Urs SCHREIBER 1h
        Synthetic prequantum field theory in a cohesive homotopy topos
        Abstract
      • 12:30
        Lunch 1h 30m
      • 14:00
        Jean BÉNABOU 1h
        Very, almost, and so on, ... (when fragments of the language find their way into Topos Theory)
      • 15:15
        General discussion 1h
      • 16:15
        Coffee break 15m
    • 16:30 18:00
      Courtes Communications - CCMJS: Courtes communications : CCMJS

      Courtes communications (30') en 2 sessions parallèles: Centre de conférences Marilyn et James Simons

      • 16:30
        Ingo BLECHSCHMIDT 30m
        Using the internal language of toposes in algebraic geometry
        Abstract
      • 17:00
        David Michael ROBERTS 30m
        Class forcing and topos theory
        Abstract
      • 17:30
        Alex SIMPSON 30m
        Probability sheaves
        Abstract
    • 16:30 18:00
      Courtes Présentations - Amphi Motchane: Courtes communications : Amphithéâtre Motchane

      Courtes communications (30') en 2 sessions parallèles : Amphithéâtre Léon Motchane

      • 16:30
        Matias I. DATA 30m Amphithéâtre Léon Motchane

        Amphithéâtre Léon Motchane

        Le Bois-Marie

        A construction of 2-filtered bicolimits of categories with 2-fibrations
        Abstract
      • 17:00
        Camell KACHOUR 30m Amphithéâtre Léon Motchane

        Amphithéâtre Léon Motchane

        Le Bois-Marie

        Globular perspective for Grothendieck ∞-topos and Grothendieck (∞,n)-topos
        Abstract
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